Experimental Investigations on Interaction of Two Drops by Thermocapillary-Buoyancy Migration

Experiments were performed, in a terrestrial environment, to study the migration and interaction of two drops with different diameters in matrix liquid under temperature gradient field. Pure soybean oil and silicon oil were used as matrix liquid and the drop liquid, respectively. The information on the motions of two drops was recorded by CCD camera system in the experiments to analyze the trajectories and velocities of the drops. Our experiments showed that, upon two drops approaching each other, the influence of the larger drop on the motion of the smaller one became significant. Meanwhile the smaller drop had a little influence on the larger one all the time. The oscillation of migration velocities of both drops was observed as they were approaching. For a short period the smaller drop even moved backward when it became side by side with the larger one during the migration. Although our experimental results on the behavior of two drops are basically consistent with the theoretical predictions, there are also apparent differences. 2006 Elsevier Ltd. All rights reserved. Keywords: Thermocapillary migration; Drop; Interaction; Oscillation 1. Introduction A bubble or drop will move when placed in another fluid with temperature gradient. This motion happens as a consequence of the variation of interfacial tension with temperature. Such a phenomenon is already known as Marangoni migration problem. With the development of microgravity science, bubble dynamics and droplet dynamics became a hot point problem of research because this investigation is very important for basic research as well as for applications in reduced gravity environment, such as space material science, chemical engineering and so on. Young et al. first investigated the thermocapillary migration of

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Flow properties of a dusty-gas point source in a supersonic free stream

By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained. It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves. In this region,formation of "multi-layer structure" in particle distribution with alternating low- and highdensity layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories.

Numerical approximation improves well survey calculation

It is now possible to improve the precision of well survey calculations by order of magnitude with numerical approximation.

Although the most precise method of simulating and calculating a wellbore trajectory generally requires more calculation than other, less-accurate methods, the wider use of computers in oil fields now eliminates this as an obstacle.

The results of various calculations show that there is a deviation of more than 10 m among the different methods of calculation for a directional well of 3,000 m.¹ Consequently, it is important to improve the precision and reliability of survey calculation-the fundamental, necessary work of quantitatively monitoring and controlling wellbore trajectories.

Dust-Cloud Structures behind a Shock Wave Moving Over a Deposited Layer of Fine Particles

The present paper investigates dispersed-phase flow structures of a dust cloud induced by a normal shock wave moving at a constant speed over a flat surface deposited with fine particles. In the shock-fitted coordinates, the general equations of dusty-gas

Planar Thermocapillary Migration of Two Bubbles in Microgravity Environment

A theoretical investigation is performed on the thermocapillary motion of two bubbles in arbitrary configuration in microgravity environment under the assumption that the surface tension is high enough to keep the bubbles spherical. The two bubbles are dr

On-Board Experimental Study Of Bubble Thermocapillary Migration In A Recoverable Satellite

An on-board space experiment of bubble thermocapillary migration was performed in the Chinese 22nd recoverable satellite in 2005. Silicone oil of nominal viscosity 5cSt was used as the continuous phase in the experiment. Air bubbles were injected into the liquid in the same direction as the constant temperature gradient in the liquid. The velocities of bubbles were obtained by recording the paths of the bubbles. The results indicate that the scaled velocity of bubbles decreases with an increase of the Marangoni number extended to 9288, which agrees with the results of previous space experiments and numerical simulation. In addition, the interaction between two bubbles was also observed in the space experiment. The trajectories and the velocities of the bubbles were obtained. The two-bubble experiment results are also consistent with the theoretical analysis.

Electrothermal stress in conductive body with collinear cracks

The temperature and stress field in a thin plate with collinear cracks interrupting an electric current field are determined. This is accomplished by using a complex function method that allows a direct means of finding the distribution of the electric current, the temperature and stress field. Temperature dependency for the heat-transfer coefficient, coefficient of linear expansion and the elastic modulus are considered. As an example, temperature distribution is calculated for an alloy (No. GH2132) plate with two collinear cracks under high temperature. Relationships between the stress, temperature, electric density and crack length are obtained. Crack trajectories emanating from existing crack are predicted by application of the strain energy density criterion which can also be used for finding the load carrying capacity of the cracked plate. (C) 2003 Elsevier Ltd. All rights reserved.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Two-way coupling model for shock-induced laminar boundary-layer flows of a dusty gas

The present paper describes a numerical two-way coupling model for shock-induced laminar boundary-layer flows of a dust-laden gas and studies the transverse migration of fine particles under the action of Saffman lift force. The governing equations are formulated in the dilute two-phase continuum framework with consideration of the finiteness of the particle Reynolds and Knudsen numbers. The full Lagrangian method is explored for calculating the dispersed-phase flow fields (including the number density of particles) in the regions of intersecting particle trajectories. The computation results show a significant reaction of the particles on the two-phase boundary-layer structure when the mass loading ratio of particles takes finite values.

Vortex dynamics in the studies of looping in tropical cyclone tracks

This paper proposes criteria for predicting the tendency of looping in tropical cyclone tracks using the approach of vortex dynamics. We model the asymmetric structure of a cyclone by a system of vortex patches. The evolution of such system of vortices is simulated by the method of contour dynamics. A new set of exact analytic formulas for contour dynamics calculations is derived, which is shown to be more computationally effective. Based on point-vortex models, we derive analytic formulas for the criteria of looping in a cyclone track. From numerical experiments, the simulated trajectories obtained from the point-vortex system and vortex patch system agree quite well. Hence, the looping criteria obtained from the point-vortex system can be applied by forecasters to stay alert for tendency of looping in a cyclone track. To demonstrate the applicability of the proposed criteria, the trajectory of Typhoon Yancy (9012), whose field data are available from ''TCM-90'', is simulated. The case study shows that the asymmetric structure similar to the pattern of a beta gyre is responsible for its recurvature when Yancy landed Fujian Province, China on 20 August 1990.

DC dielectrophoretic focusing of particles in a serpentine microchannel

Focusing particles into a tight stream is usually a necessary step prior to separating and sorting them. We present herein a proof-of-concept experiment of a novel particle focusing technique in DC electrokinetic flow through a planar serpentine microchannel. This focusing stems from the cross-stream dielectrophoretic motion induced within the channel turns. The observed particle focusing behavior is consistent with the predicted particle trajectories from a numerical modeling.